Law of total covariance

The law of total covariance is kind of like an extension of something a lot of people know about, which is sharing.

When you share something with a friend, you have to give up some of what you have, so that your friend also gets something. The law of total covariance is something like this, but with numbers.

Covariance is the measure of how two different things change together. Think about when you and your friend both got extra candy during the last holiday – the extra candy you both got changed together, so the covariance between your candy and your friend’s candy was high.

The law of total covariance says that if we have two numbers A and B, and we want to know the covariance between them, we can get the answer by calculating the covariance between A and C, plus the covariance between B and C, minus the covariance between A and B.

So if we wanted to know how two numbers changed together, we can use the law of total covariance to find out!